12 citations · 37 across the 40 of their papers we have counts for
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Pourchet's theorem in action: decomposing univariate nonnegative polynomials as sums of five squares
Victor Magron, Przemysław Koprowski, Tristan Vaccon
Pourchet proved in 1971 that every nonnegative univariate polynomial with rational coefficients is a sum of five or fewer squares. Nonetheless, there are no known algorithms for co…
Sum of Squares Decompositions of Polynomials over their Gradient Ideals with Rational Coefficients
Victor Magron, Mohab Safey El Din, Trung-Hieu Vu
Assessing non-negativity of multivariate polynomials over the reals, through the computation of {\em certificates of non-negativity}, is a topical issue in polynomial optimization.…
RealCertify: a Maple package for certifying non-negativity
Victor Magron, Mohab Safey El Din
Let (resp. ) be the field of rational (resp. real) numbers and be variables. Deciding the non-negativity of polynomials in $\mathb…
On Exact Polya and Putinar's Representations
Victor Magron, Mohab Safey El Din
We consider the problem of finding exact sums of squares (SOS) decompositions for certain classes of non-negative multivariate polynomials, relying on semidefinite programming (SDP…
Algorithms for Weighted Sums of Squares Decomposition of Non-negative Univariate Polynomials
Victor Magron, Mohab Safey El Din, Markus Schweighofer
It is well-known that every non-negative univariate real polynomial can be written as the sum of two polynomial squares with real coefficients. When one allows a weighted sum of fi…